Two people start walking at the same time in the same direction. One person walks at 7 mph and the other person walks at 4 mph. In how many hours will they be 0.75 mile(s) apart?

It'll take them 0.25 h or 15 minutes to be 0.75 miles apart at that speed.

Step-by-step explanation:

In these case we have two people that are moving in the same direction, so in order to calculate how the distance between them changes as time progress we need to calculate the relative velocity between them. When they are walking in the same direction we should subtract the greater velocity from the lesser one and when they are walking in oposite directions we should sum the velocity. In this case we need to subtract, so we have:

relative velocity = 7 - 4 = 3 mph

Since we want to know the time that they should walk in that speed in order to be separated by 0.75 miles we can use the equation bellow that describes the distance travelled in a constant velocity movement.

S = So + v*t

Where S is the final distance, So is the initial distance, v is the velocity and t is the elapsed time. We want to solve for time, so we should isolate it in the equation:

v*t = S - So

t = (S - So)/v

We assume that when they start the walking their distance is 0, so we have:

t = (0.75 - 0)/3 = 0.25 h

It'll take them 0.25 h or 15 minutes to be 0.75 miles apart at that speed.

t= 0.25 hours

Step-by-step explanation:

If the two people start walking in the same direction from a point,

their distances apart will be the difference of their distance from the starting point.

Let t be the time when they will be 0.75 miles apart

The difference of their distances = 7t-4t =3t

Therefore:

3t=0.75

t = 0.75/3

t= 0.25 hours

In 0.25 hours, they will be 0.75 miles apart.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

is there a picture

step-by-step explanation: